tan-example (used to crash)

Percentage Accurate: 79.7% → 99.7%

Time: 39.5s

Alternatives: 7

Speedup: 1.0×

Specification

\[\left(\left(\left(x = 0 \lor 0.5884142 \leq x \land x \leq 505.5909\right) \land \left(-1.796658 \cdot 10^{+308} \leq y \land y \leq -9.425585 \cdot 10^{-310} \lor 1.284938 \cdot 10^{-309} \leq y \land y \leq 1.751224 \cdot 10^{+308}\right)\right) \land \left(-1.776707 \cdot 10^{+308} \leq z \land z \leq -8.599796 \cdot 10^{-310} \lor 3.293145 \cdot 10^{-311} \leq z \land z \leq 1.725154 \cdot 10^{+308}\right)\right) \land \left(-1.796658 \cdot 10^{+308} \leq a \land a \leq -9.425585 \cdot 10^{-310} \lor 1.284938 \cdot 10^{-309} \leq a \land a \leq 1.751224 \cdot 10^{+308}\right)\]

Math

\[\begin{array}{l} \\ x + \left(\tan \left(y + z\right) - \tan a\right) \end{array} \]

FPCore

(FPCore (x y z a) :precision binary64 (+ x (- (tan (+ y z)) (tan a))))

C

double code(double x, double y, double z, double a) {
	return x + (tan((y + z)) - tan(a));
}

Fortran

real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    code = x + (tan((y + z)) - tan(a))
end function

Java

public static double code(double x, double y, double z, double a) {
	return x + (Math.tan((y + z)) - Math.tan(a));
}

Python

def code(x, y, z, a):
	return x + (math.tan((y + z)) - math.tan(a))

Julia

function code(x, y, z, a)
	return Float64(x + Float64(tan(Float64(y + z)) - tan(a)))
end

MATLAB

function tmp = code(x, y, z, a)
	tmp = x + (tan((y + z)) - tan(a));
end

Wolfram

code[x_, y_, z_, a_] := N[(x + N[(N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 79.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \left(\tan \left(y + z\right) - \tan a\right) \end{array} \]

FPCore

(FPCore (x y z a) :precision binary64 (+ x (- (tan (+ y z)) (tan a))))

C

double code(double x, double y, double z, double a) {
	return x + (tan((y + z)) - tan(a));
}

Fortran

real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    code = x + (tan((y + z)) - tan(a))
end function

Java

public static double code(double x, double y, double z, double a) {
	return x + (Math.tan((y + z)) - Math.tan(a));
}

Python

def code(x, y, z, a):
	return x + (math.tan((y + z)) - math.tan(a))

Julia

function code(x, y, z, a)
	return Float64(x + Float64(tan(Float64(y + z)) - tan(a)))
end

MATLAB

function tmp = code(x, y, z, a)
	tmp = x + (tan((y + z)) - tan(a));
end

Wolfram

code[x_, y_, z_, a_] := N[(x + N[(N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ x + \left(\frac{1}{\frac{1 - \tan y \cdot \tan z}{\tan y + \tan z}} - \tan a\right) \end{array} \]

FPCore

(FPCore (x y z a)
 :precision binary64
 (+ x (- (/ 1.0 (/ (- 1.0 (* (tan y) (tan z))) (+ (tan y) (tan z)))) (tan a))))

C

double code(double x, double y, double z, double a) {
	return x + ((1.0 / ((1.0 - (tan(y) * tan(z))) / (tan(y) + tan(z)))) - tan(a));
}

Fortran

real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    code = x + ((1.0d0 / ((1.0d0 - (tan(y) * tan(z))) / (tan(y) + tan(z)))) - tan(a))
end function

Java

public static double code(double x, double y, double z, double a) {
	return x + ((1.0 / ((1.0 - (Math.tan(y) * Math.tan(z))) / (Math.tan(y) + Math.tan(z)))) - Math.tan(a));
}

Python

def code(x, y, z, a):
	return x + ((1.0 / ((1.0 - (math.tan(y) * math.tan(z))) / (math.tan(y) + math.tan(z)))) - math.tan(a))

Julia

function code(x, y, z, a)
	return Float64(x + Float64(Float64(1.0 / Float64(Float64(1.0 - Float64(tan(y) * tan(z))) / Float64(tan(y) + tan(z)))) - tan(a)))
end

MATLAB

function tmp = code(x, y, z, a)
	tmp = x + ((1.0 / ((1.0 - (tan(y) * tan(z))) / (tan(y) + tan(z)))) - tan(a));
end

Wolfram

code[x_, y_, z_, a_] := N[(x + N[(N[(1.0 / N[(N[(1.0 - N[(N[Tan[y], $MachinePrecision] * N[Tan[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(N[Tan[y], $MachinePrecision] + N[Tan[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 77.7%

   \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
2. Add Preprocessing
3. Step-by-step derivation

   1. tan-sum 99.7%

      \[\leadsto x + \left(\color{blue}{\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z}} - \tan a\right) \]

   2. clear-num 99.7%

      \[\leadsto x + \left(\color{blue}{\frac{1}{\frac{1 - \tan y \cdot \tan z}{\tan y + \tan z}}} - \tan a\right) \]

4. Applied egg-rr 99.7%

   \[\leadsto x + \left(\color{blue}{\frac{1}{\frac{1 - \tan y \cdot \tan z}{\tan y + \tan z}}} - \tan a\right) \]
5. Add Preprocessing

Alternative 2: 99.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ x + \left(\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z} - \tan a\right) \end{array} \]

FPCore

(FPCore (x y z a)
 :precision binary64
 (+ x (- (/ (+ (tan y) (tan z)) (- 1.0 (* (tan y) (tan z)))) (tan a))))

C

double code(double x, double y, double z, double a) {
	return x + (((tan(y) + tan(z)) / (1.0 - (tan(y) * tan(z)))) - tan(a));
}

Fortran

real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    code = x + (((tan(y) + tan(z)) / (1.0d0 - (tan(y) * tan(z)))) - tan(a))
end function

Java

public static double code(double x, double y, double z, double a) {
	return x + (((Math.tan(y) + Math.tan(z)) / (1.0 - (Math.tan(y) * Math.tan(z)))) - Math.tan(a));
}

Python

def code(x, y, z, a):
	return x + (((math.tan(y) + math.tan(z)) / (1.0 - (math.tan(y) * math.tan(z)))) - math.tan(a))

Julia

function code(x, y, z, a)
	return Float64(x + Float64(Float64(Float64(tan(y) + tan(z)) / Float64(1.0 - Float64(tan(y) * tan(z)))) - tan(a)))
end

MATLAB

function tmp = code(x, y, z, a)
	tmp = x + (((tan(y) + tan(z)) / (1.0 - (tan(y) * tan(z)))) - tan(a));
end

Wolfram

code[x_, y_, z_, a_] := N[(x + N[(N[(N[(N[Tan[y], $MachinePrecision] + N[Tan[z], $MachinePrecision]), $MachinePrecision] / N[(1.0 - N[(N[Tan[y], $MachinePrecision] * N[Tan[z], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 77.7%

   \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
2. Add Preprocessing
3. Step-by-step derivation

   1. tan-sum 99.7%

      \[\leadsto x + \left(\color{blue}{\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z}} - \tan a\right) \]

   2. div-inv 99.7%

      \[\leadsto x + \left(\color{blue}{\left(\tan y + \tan z\right) \cdot \frac{1}{1 - \tan y \cdot \tan z}} - \tan a\right) \]

4. Applied egg-rr 99.7%

   \[\leadsto x + \left(\color{blue}{\left(\tan y + \tan z\right) \cdot \frac{1}{1 - \tan y \cdot \tan z}} - \tan a\right) \]
5. Step-by-step derivation

   1. associate-*r/ 99.7%

      \[\leadsto x + \left(\color{blue}{\frac{\left(\tan y + \tan z\right) \cdot 1}{1 - \tan y \cdot \tan z}} - \tan a\right) \]

   2. *-rgt-identity 99.7%

      \[\leadsto x + \left(\frac{\color{blue}{\tan y + \tan z}}{1 - \tan y \cdot \tan z} - \tan a\right) \]

6. Simplified 99.7%

   \[\leadsto x + \left(\color{blue}{\frac{\tan y + \tan z}{1 - \tan y \cdot \tan z}} - \tan a\right) \]
7. Add Preprocessing

Alternative 3: 60.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.7 \cdot 10^{-12}:\\ \;\;\;\;x + \left(\sin y - \tan a\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\tan z - \tan a\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z a)
 :precision binary64
 (if (<= y -6.7e-12) (+ x (- (sin y) (tan a))) (+ x (- (tan z) (tan a)))))

C

double code(double x, double y, double z, double a) {
	double tmp;
	if (y <= -6.7e-12) {
		tmp = x + (sin(y) - tan(a));
	} else {
		tmp = x + (tan(z) - tan(a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-6.7d-12)) then
        tmp = x + (sin(y) - tan(a))
    else
        tmp = x + (tan(z) - tan(a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double a) {
	double tmp;
	if (y <= -6.7e-12) {
		tmp = x + (Math.sin(y) - Math.tan(a));
	} else {
		tmp = x + (Math.tan(z) - Math.tan(a));
	}
	return tmp;
}

Python

def code(x, y, z, a):
	tmp = 0
	if y <= -6.7e-12:
		tmp = x + (math.sin(y) - math.tan(a))
	else:
		tmp = x + (math.tan(z) - math.tan(a))
	return tmp

Julia

function code(x, y, z, a)
	tmp = 0.0
	if (y <= -6.7e-12)
		tmp = Float64(x + Float64(sin(y) - tan(a)));
	else
		tmp = Float64(x + Float64(tan(z) - tan(a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, a)
	tmp = 0.0;
	if (y <= -6.7e-12)
		tmp = x + (sin(y) - tan(a));
	else
		tmp = x + (tan(z) - tan(a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, a_] := If[LessEqual[y, -6.7e-12], N[(x + N[(N[Sin[y], $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[Tan[z], $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -6.7000000000000001e-12

   1. Initial program 59.4%

      \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
   2. Add Preprocessing
   3. Step-by-step derivation

      1. tan-quot 59.5%

         \[\leadsto x + \left(\color{blue}{\frac{\sin \left(y + z\right)}{\cos \left(y + z\right)}} - \tan a\right) \]

      2. clear-num 59.5%

         \[\leadsto x + \left(\color{blue}{\frac{1}{\frac{\cos \left(y + z\right)}{\sin \left(y + z\right)}}} - \tan a\right) \]

   4. Applied egg-rr 59.5%

      \[\leadsto x + \left(\color{blue}{\frac{1}{\frac{\cos \left(y + z\right)}{\sin \left(y + z\right)}}} - \tan a\right) \]

   5. Taylor expanded in y around 0 29.5%

      \[\leadsto x + \left(\frac{1}{\frac{\color{blue}{\cos z + -1 \cdot \left(y \cdot \sin z\right)}}{\sin \left(y + z\right)}} - \tan a\right) \]
   6. Step-by-step derivation

      1. mul-1-neg 29.5%

         \[\leadsto x + \left(\frac{1}{\frac{\cos z + \color{blue}{\left(-y \cdot \sin z\right)}}{\sin \left(y + z\right)}} - \tan a\right) \]

      2. unsub-neg 29.5%

         \[\leadsto x + \left(\frac{1}{\frac{\color{blue}{\cos z - y \cdot \sin z}}{\sin \left(y + z\right)}} - \tan a\right) \]

      3. *-commutative 29.5%

         \[\leadsto x + \left(\frac{1}{\frac{\cos z - \color{blue}{\sin z \cdot y}}{\sin \left(y + z\right)}} - \tan a\right) \]

   7. Simplified 29.5%

      \[\leadsto x + \left(\frac{1}{\frac{\color{blue}{\cos z - \sin z \cdot y}}{\sin \left(y + z\right)}} - \tan a\right) \]

   8. Taylor expanded in z around 0 30.3%

      \[\leadsto x + \left(\color{blue}{\sin y} - \tan a\right) \]

   if -6.7000000000000001e-12 < y

   1. Initial program 84.1%

      \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0 73.7%

      \[\leadsto \color{blue}{\left(x + \frac{\sin z}{\cos z}\right) - \frac{\sin a}{\cos a}} \]
   4. Step-by-step derivation

      1. +-commutative 73.7%

         \[\leadsto \color{blue}{\left(\frac{\sin z}{\cos z} + x\right)} - \frac{\sin a}{\cos a} \]

      2. associate--l+ 73.7%

         \[\leadsto \color{blue}{\frac{\sin z}{\cos z} + \left(x - \frac{\sin a}{\cos a}\right)} \]

   5. Simplified 73.7%

      \[\leadsto \color{blue}{\frac{\sin z}{\cos z} + \left(x - \frac{\sin a}{\cos a}\right)} \]
   6. Step-by-step derivation

      1. tan-quot 73.7%

         \[\leadsto \color{blue}{\tan z} + \left(x - \frac{\sin a}{\cos a}\right) \]

      2. tan-quot 73.7%

         \[\leadsto \tan z + \left(x - \color{blue}{\tan a}\right) \]

      3. associate-+r- 73.7%

         \[\leadsto \color{blue}{\left(\tan z + x\right) - \tan a} \]

   7. Applied egg-rr 73.7%

      \[\leadsto \color{blue}{\left(\tan z + x\right) - \tan a} \]
   8. Step-by-step derivation

      1. +-commutative 73.7%

         \[\leadsto \color{blue}{\left(x + \tan z\right)} - \tan a \]

      2. associate--l+ 73.7%

         \[\leadsto \color{blue}{x + \left(\tan z - \tan a\right)} \]

   9. Simplified 73.7%

      \[\leadsto \color{blue}{x + \left(\tan z - \tan a\right)} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 4: 79.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \left(\tan \left(y + z\right) - \tan a\right) \end{array} \]

FPCore

(FPCore (x y z a) :precision binary64 (+ x (- (tan (+ y z)) (tan a))))

C

double code(double x, double y, double z, double a) {
	return x + (tan((y + z)) - tan(a));
}

Fortran

real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    code = x + (tan((y + z)) - tan(a))
end function

Java

public static double code(double x, double y, double z, double a) {
	return x + (Math.tan((y + z)) - Math.tan(a));
}

Python

def code(x, y, z, a):
	return x + (math.tan((y + z)) - math.tan(a))

Julia

function code(x, y, z, a)
	return Float64(x + Float64(tan(Float64(y + z)) - tan(a)))
end

MATLAB

function tmp = code(x, y, z, a)
	tmp = x + (tan((y + z)) - tan(a));
end

Wolfram

code[x_, y_, z_, a_] := N[(x + N[(N[Tan[N[(y + z), $MachinePrecision]], $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 77.7%

   \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
2. Add Preprocessing
3. Add Preprocessing

Alternative 5: 42.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \left(\sin y - \tan a\right) \end{array} \]

FPCore

(FPCore (x y z a) :precision binary64 (+ x (- (sin y) (tan a))))

C

double code(double x, double y, double z, double a) {
	return x + (sin(y) - tan(a));
}

Fortran

real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    code = x + (sin(y) - tan(a))
end function

Java

public static double code(double x, double y, double z, double a) {
	return x + (Math.sin(y) - Math.tan(a));
}

Python

def code(x, y, z, a):
	return x + (math.sin(y) - math.tan(a))

Julia

function code(x, y, z, a)
	return Float64(x + Float64(sin(y) - tan(a)))
end

MATLAB

function tmp = code(x, y, z, a)
	tmp = x + (sin(y) - tan(a));
end

Wolfram

code[x_, y_, z_, a_] := N[(x + N[(N[Sin[y], $MachinePrecision] - N[Tan[a], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 77.7%

   \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
2. Add Preprocessing
3. Step-by-step derivation

   1. tan-quot 77.7%

      \[\leadsto x + \left(\color{blue}{\frac{\sin \left(y + z\right)}{\cos \left(y + z\right)}} - \tan a\right) \]

   2. clear-num 77.7%

      \[\leadsto x + \left(\color{blue}{\frac{1}{\frac{\cos \left(y + z\right)}{\sin \left(y + z\right)}}} - \tan a\right) \]

4. Applied egg-rr 77.7%

   \[\leadsto x + \left(\color{blue}{\frac{1}{\frac{\cos \left(y + z\right)}{\sin \left(y + z\right)}}} - \tan a\right) \]

5. Taylor expanded in y around 0 62.5%

   \[\leadsto x + \left(\frac{1}{\frac{\color{blue}{\cos z + -1 \cdot \left(y \cdot \sin z\right)}}{\sin \left(y + z\right)}} - \tan a\right) \]
6. Step-by-step derivation

   1. mul-1-neg 62.5%

      \[\leadsto x + \left(\frac{1}{\frac{\cos z + \color{blue}{\left(-y \cdot \sin z\right)}}{\sin \left(y + z\right)}} - \tan a\right) \]

   2. unsub-neg 62.5%

      \[\leadsto x + \left(\frac{1}{\frac{\color{blue}{\cos z - y \cdot \sin z}}{\sin \left(y + z\right)}} - \tan a\right) \]

   3. *-commutative 62.5%

      \[\leadsto x + \left(\frac{1}{\frac{\cos z - \color{blue}{\sin z \cdot y}}{\sin \left(y + z\right)}} - \tan a\right) \]

7. Simplified 62.5%

   \[\leadsto x + \left(\frac{1}{\frac{\color{blue}{\cos z - \sin z \cdot y}}{\sin \left(y + z\right)}} - \tan a\right) \]

8. Taylor expanded in z around 0 42.7%

   \[\leadsto x + \left(\color{blue}{\sin y} - \tan a\right) \]
9. Add Preprocessing

Alternative 6: 31.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \log \left(e^{x}\right) \end{array} \]

FPCore

(FPCore (x y z a) :precision binary64 (log (exp x)))

C

double code(double x, double y, double z, double a) {
	return log(exp(x));
}

Fortran

real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    code = log(exp(x))
end function

Java

public static double code(double x, double y, double z, double a) {
	return Math.log(Math.exp(x));
}

Python

def code(x, y, z, a):
	return math.log(math.exp(x))

Julia

function code(x, y, z, a)
	return log(exp(x))
end

MATLAB

function tmp = code(x, y, z, a)
	tmp = log(exp(x));
end

Wolfram

code[x_, y_, z_, a_] := N[Log[N[Exp[x], $MachinePrecision]], $MachinePrecision]

Derivation

1. Initial program 77.7%

   \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
2. Add Preprocessing
3. Step-by-step derivation

   1. add-cbrt-cube 77.2%

      \[\leadsto \color{blue}{\sqrt[3]{\left(\left(x + \left(\tan \left(y + z\right) - \tan a\right)\right) \cdot \left(x + \left(\tan \left(y + z\right) - \tan a\right)\right)\right) \cdot \left(x + \left(\tan \left(y + z\right) - \tan a\right)\right)}} \]

   2. pow1/3 71.8%

      \[\leadsto \color{blue}{{\left(\left(\left(x + \left(\tan \left(y + z\right) - \tan a\right)\right) \cdot \left(x + \left(\tan \left(y + z\right) - \tan a\right)\right)\right) \cdot \left(x + \left(\tan \left(y + z\right) - \tan a\right)\right)\right)}^{0.3333333333333333}} \]

   3. pow3 71.8%

      \[\leadsto {\color{blue}{\left({\left(x + \left(\tan \left(y + z\right) - \tan a\right)\right)}^{3}\right)}}^{0.3333333333333333} \]

   4. +-commutative 71.8%

      \[\leadsto {\left({\color{blue}{\left(\left(\tan \left(y + z\right) - \tan a\right) + x\right)}}^{3}\right)}^{0.3333333333333333} \]

   5. associate-+l- 71.8%

      \[\leadsto {\left({\color{blue}{\left(\tan \left(y + z\right) - \left(\tan a - x\right)\right)}}^{3}\right)}^{0.3333333333333333} \]

4. Applied egg-rr 71.8%

   \[\leadsto \color{blue}{{\left({\left(\tan \left(y + z\right) - \left(\tan a - x\right)\right)}^{3}\right)}^{0.3333333333333333}} \]

5. Taylor expanded in x around inf 31.4%

   \[\leadsto {\color{blue}{\left({x}^{3}\right)}}^{0.3333333333333333} \]
6. Step-by-step derivation

   1. add-log-exp 31.4%

      \[\leadsto \color{blue}{\log \left(e^{{\left({x}^{3}\right)}^{0.3333333333333333}}\right)} \]

   2. pow-pow 31.6%

      \[\leadsto \log \left(e^{\color{blue}{{x}^{\left(3 \cdot 0.3333333333333333\right)}}}\right) \]

   3. metadata-eval 31.6%

      \[\leadsto \log \left(e^{{x}^{\color{blue}{1}}}\right) \]

   4. pow1 31.6%

      \[\leadsto \log \left(e^{\color{blue}{x}}\right) \]

7. Applied egg-rr 31.6%

   \[\leadsto \color{blue}{\log \left(e^{x}\right)} \]
8. Add Preprocessing

Alternative 7: 31.8% accurate, 207.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z a) :precision binary64 x)

C

double code(double x, double y, double z, double a) {
	return x;
}

Fortran

real(8) function code(x, y, z, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: a
    code = x
end function

Java

public static double code(double x, double y, double z, double a) {
	return x;
}

Python

def code(x, y, z, a):
	return x

Julia

function code(x, y, z, a)
	return x
end

MATLAB

function tmp = code(x, y, z, a)
	tmp = x;
end

Wolfram

code[x_, y_, z_, a_] := x

Derivation

1. Initial program 77.7%

   \[x + \left(\tan \left(y + z\right) - \tan a\right) \]
2. Add Preprocessing

3. Taylor expanded in x around inf 31.6%

   \[\leadsto \color{blue}{x} \]
4. Add Preprocessing

Reproduce

herbie shell --seed 2024085 
(FPCore (x y z a)
  :name "tan-example (used to crash)"
  :precision binary64
  :pre (and (and (and (or (== x 0.0) (and (<= 0.5884142 x) (<= x 505.5909))) (or (and (<= -1.796658e+308 y) (<= y -9.425585e-310)) (and (<= 1.284938e-309 y) (<= y 1.751224e+308)))) (or (and (<= -1.776707e+308 z) (<= z -8.599796e-310)) (and (<= 3.293145e-311 z) (<= z 1.725154e+308)))) (or (and (<= -1.796658e+308 a) (<= a -9.425585e-310)) (and (<= 1.284938e-309 a) (<= a 1.751224e+308))))
  (+ x (- (tan (+ y z)) (tan a))))